Bayesian spatial survival modelling for dengue fever in Makassar, Indonesia
Sri Astuti Thamrina,
, Aswib, Ansariadic, Andi Kresna Jayaa, Kerrie Mengersend
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a Department of Statistics, Hasanuddin University, Makassar 90245, Indonesia
b Statistics Study Program, Universitas Negeri Makassar, Makassar 90224, Indonesia
c Department of Epidemiology, Hasanuddin University, Makassar 90245, Indonesia
d School of Mathematical Science, Queensland University of Technology, Brisbane 4000, Australia
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"apellidos" => "Lagu" ] 3 => array:1 [ "apellidos" => "Habibi" ] 4 => array:1 [ "apellidos" => "Sukfitrianty" ] 5 => array:2 [ "nombre" => "Syamsul" "apellidos" => "Alam" ] ] ] ] ] "idiomaDefecto" => "en" "EPUB" => "https://multimedia.elsevier.es/PublicationsMultimediaV1/item/epub/S0213911120302739?idApp=WGSE" "url" => "/02139111/00000035000000S1/v1_202104060920/S0213911120302739/v1_202104060920/en/main.assets" ] "en" => array:19 [ "idiomaDefecto" => true "titulo" => "Bayesian spatial survival modelling for dengue fever in Makassar, Indonesia" "tieneTextoCompleto" => true "paginas" => array:1 [ 0 => array:2 [ "paginaInicial" => "S59" "paginaFinal" => "S63" ] ] "autores" => array:1 [ 0 => array:4 [ "autoresLista" => "Sri Astuti Thamrin, Aswi, Ansariadi, Andi Kresna Jaya, Kerrie Mengersen" "autores" => array:5 [ 0 => array:4 [ "nombre" => "Sri Astuti" "apellidos" => "Thamrin" "email" => array:2 [ 0 => "tuti@unhas.ac.id" 1 => "pmc@agri.unhas.ac.id" ] "referencia" => array:2 [ 0 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">a</span>" "identificador" => "aff0005" ] 1 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">*</span>" "identificador" => "cor0005" ] ] ] 1 => array:2 [ "apellidos" => "Aswi" "referencia" => array:1 [ 0 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">b</span>" "identificador" => "aff0010" ] ] ] 2 => array:2 [ "apellidos" => "Ansariadi" "referencia" => array:1 [ 0 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">c</span>" "identificador" => "aff0015" ] ] ] 3 => array:3 [ "nombre" => "Andi Kresna" "apellidos" => "Jaya" "referencia" => array:1 [ 0 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">a</span>" "identificador" => "aff0005" ] ] ] 4 => array:3 [ "nombre" => "Kerrie" "apellidos" => "Mengersen" "referencia" => array:1 [ 0 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">d</span>" "identificador" => "aff0020" ] ] ] ] "afiliaciones" => array:4 [ 0 => array:3 [ "entidad" => "Department of Statistics, Hasanuddin University, Makassar 90245, Indonesia" "etiqueta" => "a" "identificador" => "aff0005" ] 1 => array:3 [ "entidad" => "Statistics Study Program, Universitas Negeri Makassar, Makassar 90224, Indonesia" "etiqueta" => "b" "identificador" => "aff0010" ] 2 => array:3 [ "entidad" => "Department of Epidemiology, Hasanuddin University, Makassar 90245, Indonesia" "etiqueta" => "c" "identificador" => "aff0015" ] 3 => array:3 [ "entidad" => "School of Mathematical Science, Queensland University of Technology, Brisbane 4000, Australia" "etiqueta" => "d" "identificador" => "aff0020" ] ] "correspondencia" => array:1 [ 0 => array:3 [ "identificador" => "cor0005" "etiqueta" => "⁎" "correspondencia" => "Corresponding author." ] ] ] ] "resumenGrafico" => array:2 [ "original" => 0 "multimedia" => array:7 [ "identificador" => "fig0020" "etiqueta" => "Figure 4" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr4.jpeg" "Alto" => 825 "Ancho" => 2508 "Tamanyo" => 123788 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0040" class="elsevierStyleSimplePara elsevierViewall">Posterior densities plots of the significant parameter for DF survival data in the Makassar city, Indonesia.</p>" ] ] ] "textoCompleto" => "<span class="elsevierStyleSections"><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0035">Introduction</span><p id="par0005" class="elsevierStylePara elsevierViewall">Dengue fever (DF) is a disease that often causes outbreaks or epidemics. The recent report from the World Health Organization<a class="elsevierStyleCrossRef" href="#bib0130"><span class="elsevierStyleSup">1</span></a> reported that globally, there has been a significant increase in the number of DF every year. Indeed, Indonesia has the most cases of DF disease in Southeast Asia region with more than 129,650 people infected with the virus in 2015.<a class="elsevierStyleCrossRef" href="#bib0135"><span class="elsevierStyleSup">2</span></a> Makassar city is one of the areas in Indonesia that has DF virus each year. There is a real need to increase efforts to prevent transmission of the disease and reduce the mortality rate.</p><p id="par0010" class="elsevierStylePara elsevierViewall">Efforts to reduce the death rate from DF virus can be either preventive or curative. An example of a preventive method is raising awareness and a healthy lifestyle to reduce the incidence and spread of DF.<a class="elsevierStyleCrossRef" href="#bib0140"><span class="elsevierStyleSup">3</span></a> An example of a curative method is providing the right medical treatment to patients. Here, the issue of survival of patients with DF becomes important to investigate.</p><p id="par0015" class="elsevierStylePara elsevierViewall">Survival time of patients with DF disease can be influenced by many factors. So far in the literature, in general, the factors can be grouped into two major themes. The first theme is associated with physical or biological characteristics of DF patients such as age, gender, etc.<a class="elsevierStyleCrossRef" href="#bib0130"><span class="elsevierStyleSup">1</span></a> The second theme covers a number of non-biological factors such as location, local conditions, rainfall, socio-economic conditions and therapy or treatment given to patients with DF.<a class="elsevierStyleCrossRefs" href="#bib0145"><span class="elsevierStyleSup">4-7</span></a></p><p id="par0020" class="elsevierStylePara elsevierViewall">Survival data are commonly analyzed using proportional hazards regression.<a class="elsevierStyleCrossRefs" href="#bib0165"><span class="elsevierStyleSup">8–10</span></a> However, this method is based on a relatively simple model and it does not allow the incorporation of external information such as survival spatial information. Bayesian approaches to modelling and analysis of DF have become increasingly popular over the last decade. For example, Honorato et al.<a class="elsevierStyleCrossRef" href="#bib0180"><span class="elsevierStyleSup">11</span></a> investigated cases of DF which were spatially distributed in Brazil using a Bayesian spatial hierarchical model using conditional autoregressive (CAR) prior. Lowe et al.<a class="elsevierStyleCrossRef" href="#bib0185"><span class="elsevierStyleSup">12</span></a> used a general spatio-temporal mixed model with a Bayesian framework taking into account geographical and temporal resolution to evaluate the spread of DF in Brazil Southeast. Furthermore, Jaya et al.<a class="elsevierStyleCrossRef" href="#bib0190"><span class="elsevierStyleSup">13</span></a> used a Bayesian spatial approach to model and map the DF cases in Bandung, Indonesia.</p><p id="par0025" class="elsevierStylePara elsevierViewall">As noted above, most of this literature focuses on incidence and there are fewer papers on DF survival. The literature on spatial modelling of DF survival is even more sparse and limited to small-scale studies.<a class="elsevierStyleCrossRefs" href="#bib0195"><span class="elsevierStyleSup">14–18</span></a> For example, Thamrin and Taufik<a class="elsevierStyleCrossRef" href="#bib0195"><span class="elsevierStyleSup">14</span></a> used multilevel survival to study DF survival. Aswi et al.<a class="elsevierStyleCrossRef" href="#bib0215"><span class="elsevierStyleSup">18</span></a> considered DF survival in a single hospital in Makassar using Bayesian Weibull survival and a semiparametric Cox proportional hazards model. In this study, a Bayesian spatial survival method via a CAR approach was used to analyze DF patients’ survival, and to investigate factors that influence DF patients’ survival. This is investigated through a DF patients’ survival in Makassar, Indonesia.</p></span><span id="sec0010" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0040">Methods</span><span id="sec0015" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0045">Study area and source of data</span><p id="par0030" class="elsevierStylePara elsevierViewall">Makassar is the most populous city in South Sulawesi or even in the eastern part of Indonesia.<a class="elsevierStyleCrossRef" href="#bib0220"><span class="elsevierStyleSup">19</span></a> Makassar city consists of 14 sub-districts with 143 villages in these sub-districts (<a class="elsevierStyleCrossRef" href="#fig0005">Figure 1</a>).<a class="elsevierStyleCrossRef" href="#bib0225"><span class="elsevierStyleSup">20</span></a></p><elsevierMultimedia ident="fig0005"></elsevierMultimedia><p id="par0035" class="elsevierStylePara elsevierViewall">Data used were collected from four big hospitals in Makassar city, that is, Dr. Wahidin Sudirohusodo, Labuang Baji, Pelamonia, and Haji Hospitals. In this dataset, the variables used were sex, haematocrit, leukocyte, haemoglobin, thrombocyte, level severity of DF type (grade), age, survival time, and address of DF patients. The number of patients diagnosed with DF were treated in these hospitals, in the period of January 2015 to May 2017 is 934.</p><p id="par0040" class="elsevierStylePara elsevierViewall">In our models, the survival response variable <span class="elsevierStyleItalic">t</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">ij</span></span> is defined as the number of days that a patient stayed in the hospital until they recovered or got consent to leave the hospital or death. The DF patients self-discharge or transfer to another hospital and still alive at the end of the study period were treated as ‘censored’. The DF incidence rates, which is the number of cases per 10,000 people per year, for each sub-district from the four big hospitals in Makassar city are presented in <a class="elsevierStyleCrossRef" href="#fig0010">Figure 2</a>. Data on population numbers for the same time period were collected from the Central Bureau of Statistics of Makassar city, Indonesia.<a class="elsevierStyleCrossRef" href="#bib0220"><span class="elsevierStyleSup">19</span></a> The population size was used to calculate and to map the hazard rate.</p><elsevierMultimedia ident="fig0010"></elsevierMultimedia></span><span id="sec0020" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0050">Spatial survival model</span><p id="par0045" class="elsevierStylePara elsevierViewall">Following the description in Banerjee et al.,<a class="elsevierStyleCrossRef" href="#bib0210"><span class="elsevierStyleSup">17</span></a> let tij be the response described in the previous section, namely time to recovery for subject <span class="elsevierStyleItalic">j</span> in sub-district <span class="elsevierStyleItalic">i</span>, j=1,2,…,ni, i=1,2,…,l. Let <span class="elsevierStyleItalic">x</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">ij</span></span> be the corresponding vector of individual-specific covariates. Assume a proportional hazard h(tij;xij) that follows a Weibull distribution with h0(tij)=ρtijρ−1 as follows:<elsevierMultimedia ident="eq0005"></elsevierMultimedia>h0(tij) represents a baseline hazard. The exponential term involving the covariates affect the baseline hazard multiplicatively. Here, ρ is the shape parameter of the baseline hazard and the vector β contains the intercept for the baseline hazard. The parameter ρ represents monotonicity of the hazard rate in the Weibull mode,<a class="elsevierStyleCrossRef" href="#bib0230"><span class="elsevierStyleSup">21</span></a> where ρ=1 represents a constant hazard rate, and ρ>1 and ρ<1 indicate that the hazard will increase and decrease monotonically with time, respectively. Since Wi=log ωi, in the frailty setting,<a class="elsevierStyleCrossRef" href="#bib0235"><span class="elsevierStyleSup">22</span></a> Eq. <a class="elsevierStyleCrossRef" href="#eq0005">(1)</a> is extended to:<elsevierMultimedia ident="eq0010"></elsevierMultimedia></p><p id="par0125" class="elsevierStylePara elsevierViewall"><span class="elsevierStyleItalic">W</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i</span></span> is the sub-district-specific frailty term with distribution:<elsevierMultimedia ident="eq0015"></elsevierMultimedia><elsevierMultimedia ident="eq0020"></elsevierMultimedia><elsevierMultimedia ident="eq0025"></elsevierMultimedia><elsevierMultimedia ident="eq0030"></elsevierMultimedia><elsevierMultimedia ident="eq0035"></elsevierMultimedia>where log (μ)=β0+βx. CAR denotes a conditionally autoregressive structure Wi|Wi′≠i∼N(W¯i,1/λmi)17,22 and λ is the CAR parameter in Eq. <a class="elsevierStyleCrossRef" href="#eq0015">(3)</a> which states the<elsevierMultimedia ident="eq0040"></elsevierMultimedia>where <span class="elsevierStyleItalic">i</span> adj <span class="elsevierStyleItalic">i</span>′ denotes regions <span class="elsevierStyleItalic">i</span>′ that are adjacent to region <span class="elsevierStyleItalic">i</span>, W¯i is the average of the Wi≠i′ that are adjacent to <span class="elsevierStyleItalic">W</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i</span></span>, and <span class="elsevierStyleItalic">m</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">i</span></span> is the number of these adjacencies.</p><p id="par0050" class="elsevierStylePara elsevierViewall">To complete the Bayesian model specification in Eq. <a class="elsevierStyleCrossRef" href="#eq0040">(4)</a>, we use prior distributions on ρ, β and σ2. We use a gamma hyperprior distribution for λ. With this parameter, the gamma distribution has mean 1 and the variance 1; see Banerjee et al.<a class="elsevierStyleCrossRef" href="#bib0210"><span class="elsevierStyleSup">17</span></a> In this paper, we include both spatial and non-spatial frailties.<a class="elsevierStyleCrossRef" href="#bib0210"><span class="elsevierStyleSup">17</span></a> Non-spatial frailties means that the model has an unstructured frailty term, expressed as independently and identically distributed (i.i.d) N(0,σ2). The model was fitted using the OpenBUGS software.<a class="elsevierStyleCrossRef" href="#bib0240"><span class="elsevierStyleSup">23</span></a> The MCMC algorithm was run with 150,000 iterations, discarding 10,000 as burn-in. Monitoring MCMC convergence was done through trace plots, autocorrelation plots, and plots of the posterior distributions of the model parameters.</p><p id="par0055" class="elsevierStylePara elsevierViewall">Goodness of fit measures were used to test whether a spatial survival model adequately represents the data. The deviance information criterion (DIC)<a class="elsevierStyleCrossRef" href="#bib0245"><span class="elsevierStyleSup">24</span></a> is one of the criteria in evaluating the best model for several data sets using the Bayesian approach. A model is more suitable when it has the smallest DIC.<a class="elsevierStyleCrossRef" href="#bib0245"><span class="elsevierStyleSup">24</span></a></p></span></span><span id="sec0025" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0055">Results</span><p id="par0060" class="elsevierStylePara elsevierViewall">The model was fitted to DF survival dataset as described in Section “Spatial Survival Model”. By using the different set of starting values, the chain was run. Convergence can be assessed whether it has been achieved or not through the MCMC chain. The results of the hazard rates obtained from Eq. <a class="elsevierStyleCrossRef" href="#eq0010">(2)</a> were mapped using the Map tool R version 4.0.2 package.</p><p id="par0065" class="elsevierStylePara elsevierViewall">According to <a class="elsevierStyleCrossRef" href="#fig0005">Figure 1</a>, the city of Makassar is divided into 14 sub-districts so a spatial weights matrix of queen contiguity order one of 14×14 was formed. The corresponding adjacency matrix for Makassar city, Indonesia is shown in <a class="elsevierStyleCrossRef" href="#fig0015">Figure 3</a>. The Weibull assumption for the survival time was assessed by plotting log[−log(<span class="elsevierStyleItalic">S</span>(<span class="elsevierStyleItalic">t</span>))] versus log(<span class="elsevierStyleItalic">t</span>), where the survival probability <span class="elsevierStyleItalic">S</span>(<span class="elsevierStyleItalic">t</span>) was obtained using Kaplan–Meier estimation and <span class="elsevierStyleItalic">t</span> is the survival time. The Weibull distribution was indicated by a straight line plot. This assumption was also verified by application of the Mann test (if <span class="elsevierStyleItalic">F</span><span class="elsevierStyleInf">approximation</span><span class="elsevierStyleHsp" style=""></span>=<span class="elsevierStyleHsp" style=""></span>0.784<span class="elsevierStyleHsp" style=""></span><<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleItalic">F</span><span class="elsevierStyleInf">criterion</span><span class="elsevierStyleHsp" style=""></span>=<span class="elsevierStyleHsp" style=""></span>1.17 at the 5% level, then the null hypothesis is accepted). The Weibull distribution was thus considered to be appropriate for these data.</p><elsevierMultimedia ident="fig0015"></elsevierMultimedia><p id="par0070" class="elsevierStylePara elsevierViewall">From <a class="elsevierStyleCrossRefs" href="#fig0020">Figures 4 and 5</a>, the MCMC outputs for the significant parameters of the model in the form of posterior density and trace plots show a well-behaved and fast mixing process. The posterior estimates of parameters and corresponding 95% confidence intervals (CI) are presented in <a class="elsevierStyleCrossRef" href="#tbl0005">Table 1</a>. It can be inferred that age and grade substantially describe patients’ survival times. The variables age and grade both have a negative effect on the expected survival time. For example, an increase of one year in patient's age increased the hazard at DF survival by exp(−0.006)<span class="elsevierStyleHsp" style=""></span>=<span class="elsevierStyleHsp" style=""></span>0.994 days.</p><elsevierMultimedia ident="fig0020"></elsevierMultimedia><elsevierMultimedia ident="fig0025"></elsevierMultimedia><elsevierMultimedia ident="tbl0005"></elsevierMultimedia><p id="par0075" class="elsevierStylePara elsevierViewall"><a class="elsevierStyleCrossRef" href="#tbl0010">Table 2</a> provides a summary of model fit with a corresponding non-spatial survival model as a comparison. In the latter, Eq. <a class="elsevierStyleCrossRef" href="#eq0015">(3)</a> is replaced by Wi∼N(0,σ2). The spatial model is more suitable for these data. This is indicated by the larger size of the effective parameter pD and the smaller value of DIC.</p><elsevierMultimedia ident="tbl0010"></elsevierMultimedia><p id="par0080" class="elsevierStylePara elsevierViewall">The mapped summary of the posterior mean survival times per sub-district is shown in <a class="elsevierStyleCrossRef" href="#fig0030">Figure 6</a>. The results indicate that regional sub-districts located around urban centres, namely Mariso had the lowest hazard rate. The constant hazard rates occurred in the sub-districts Manggala, Panakkukang, Bontoala, Rappocini, Tamalanrea, and Wajo. The higher hazard rate of DF patients occurred in the sub-districts Biringkanaya, Makassar and Mamajang.</p><elsevierMultimedia ident="fig0030"></elsevierMultimedia><p id="par0085" class="elsevierStylePara elsevierViewall">The Kaplan–Meier curve for DF survival with covariates age and grade is shown in <a class="elsevierStyleCrossRef" href="#fig0035">Figure 7</a>. The covariates were established for survival time in the first patient for DF. The probability of survival for this first patient is predicted to fall fairly rapidly towards 0.10 when the survival time is about 2 days, then declines very slowly thereafter.</p><elsevierMultimedia ident="fig0035"></elsevierMultimedia></span><span id="sec0030" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0060">Discussion</span><p id="par0090" class="elsevierStylePara elsevierViewall">We have presented the modelling of the spatial correlated survival data in this paper. To estimate spatial survival with a CAR model, a Bayesian model via a MCMC computational technique was used. The case study used the survival times of DF patients from hospitals in Makassar, Indonesia for the period 2015–2017 with covariates.</p><p id="par0095" class="elsevierStylePara elsevierViewall">Overall, the results of this study indicated that age and grade factors appear to influence the number of days of patients hospitalised with DF until they got recovery or were allowed to go home. The prediction of DF patients’ survival time based on influencing variables is also illustrated. This suggests that when the survival time is about 2 days, the probability of patient's survival time drops fairly rapidly towards 0.10 and decays very slowly thereafter. Mariso had the lowest hazard rate while Biringkanaya had the highest hazard rate, fooled by Makassar and Mamajang. These districts are the potential regions to target for health policy intervention in high risk areas and for more targeted, efficient allocation of the relevant resources. Notwithstanding this, further investigation is needed in order to consider socio economic, temperature, and humidity effects in modelling the survival factors.<a class="elsevierStyleCrossRefs" href="#bib0150"><span class="elsevierStyleSup">5–7,12</span></a> The flexibility of the Bayesian spatial survival models invites extensions to more complicated scenarios such as a spatial clustering<a class="elsevierStyleCrossRef" href="#bib0155"><span class="elsevierStyleSup">6</span></a> and spatial-temporal model.<a class="elsevierStyleCrossRefs" href="#bib0150"><span class="elsevierStyleSup">5,25</span></a></p></span><span id="sec0035" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0065">Conclusions</span><p id="par0100" class="elsevierStylePara elsevierViewall">The relative risk map and related factors of DF patients’ survival can indicate the health policy makers to give special attention to the high risk areas in order to faster and more targeted treatment.</p></span><span id="sec0040" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0070">Authorship contributions</span><p id="par0105" class="elsevierStylePara elsevierViewall">SAT contributed to the concept and design of the study, carried out statistical analysis and wrote manuscripts. AS and KM interpreted the data, analyzed and wrote the manuscript. AKJ carried out the statistical analysis and AN collects the necessary data. All authors read and approved the final manuscript.</p></span><span id="sec0045" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0075">Conflicts of interest</span><p id="par0110" class="elsevierStylePara elsevierViewall">The authors declare that there is no conflict of interests.</p></span></span>" "textoCompletoSecciones" => array:1 [ "secciones" => array:11 [ 0 => array:3 [ "identificador" => "xres1492591" "titulo" => "Abstract" "secciones" => array:4 [ 0 => array:2 [ "identificador" => "abst0005" "titulo" => "Objective" ] 1 => array:2 [ "identificador" => "abst0010" "titulo" => "Method" ] 2 => array:2 [ "identificador" => "abst0015" "titulo" => "Results" ] 3 => array:2 [ "identificador" => "abst0020" "titulo" => "Conclusions" ] ] ] 1 => array:2 [ "identificador" => "xpalclavsec1355234" "titulo" => "Keywords" ] 2 => array:2 [ "identificador" => "sec0005" "titulo" => "Introduction" ] 3 => array:3 [ "identificador" => "sec0010" "titulo" => "Methods" "secciones" => array:2 [ 0 => array:2 [ "identificador" => "sec0015" "titulo" => "Study area and source of data" ] 1 => array:2 [ "identificador" => "sec0020" "titulo" => "Spatial survival model" ] ] ] 4 => array:2 [ "identificador" => "sec0025" "titulo" => "Results" ] 5 => array:2 [ "identificador" => "sec0030" "titulo" => "Discussion" ] 6 => array:2 [ "identificador" => "sec0035" "titulo" => "Conclusions" ] 7 => array:2 [ "identificador" => "sec0040" "titulo" => "Authorship contributions" ] 8 => array:2 [ "identificador" => "sec0045" "titulo" => "Conflicts of interest" ] 9 => array:2 [ "identificador" => "xack522572" "titulo" => "Acknowledgements" ] 10 => array:1 [ "titulo" => "References" ] ] ] "pdfFichero" => "main.pdf" "tienePdf" => true "fechaRecibido" => "2020-08-24" "fechaAceptado" => "2020-12-04" "PalabrasClave" => array:1 [ "en" => array:1 [ 0 => array:4 [ "clase" => "keyword" "titulo" => "Keywords" "identificador" => "xpalclavsec1355234" "palabras" => array:5 [ 0 => "Conditional autoregressive" 1 => "Dengue fever" 2 => "Hazard rate" 3 => "Spatial survival" 4 => "Weibull model" ] ] ] ] "tieneResumen" => true "resumen" => array:1 [ "en" => array:3 [ "titulo" => "Abstract" "resumen" => "<span id="abst0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0010">Objective</span><p id="spar0005" class="elsevierStyleSimplePara elsevierViewall">To understand the spatial pattern of dengue fever (DF) patients’ survival and investigated factors influencing DF patients’ survival.</p></span> <span id="abst0010" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0015">Method</span><p id="spar0010" class="elsevierStyleSimplePara elsevierViewall">A Bayesian spatial survival method via a conditional autoregressive approach was used to analyze the factors that influence DF patients’ survival in 14 sub-districts from January 2015 to May 2017 in Makassar city, Indonesia. Bayesian spatial and a non-spatial model were compared by using deviance information criterion.</p></span> <span id="abst0015" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0020">Results</span><p id="spar0015" class="elsevierStyleSimplePara elsevierViewall">The spatial model was more suitable than a non-spatial model. Under the Bayesian spatial model, there was a substantive relationship between age, grade and DF patients’ survival time.</p></span> <span id="abst0020" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0025">Conclusions</span><p id="spar0020" class="elsevierStyleSimplePara elsevierViewall">The relative risk map and related factors of DF patients’ survival can indicate the health policy makers to give special attention to the high risk areas in order to faster and more targeted treatment.</p></span>" "secciones" => array:4 [ 0 => array:2 [ "identificador" => "abst0005" "titulo" => "Objective" ] 1 => array:2 [ "identificador" => "abst0010" "titulo" => "Method" ] 2 => array:2 [ "identificador" => "abst0015" "titulo" => "Results" ] 3 => array:2 [ "identificador" => "abst0020" "titulo" => "Conclusions" ] ] ] ] "NotaPie" => array:1 [ 0 => array:2 [ "etiqueta" => "☆" "nota" => "<p class="elsevierStyleNotepara" id="npar0005">Peer-review under responsibility of the scientific committee of the 1st International Conference on Safety and Public Health (ICOS-PH 2020). Full-text and the content of it is under responsibility of authors of the article.</p>" ] ] "multimedia" => array:17 [ 0 => array:7 [ "identificador" => "fig0005" "etiqueta" => "Figure 1" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr1.jpeg" "Alto" => 949 "Ancho" => 1500 "Tamanyo" => 137974 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0025" class="elsevierStyleSimplePara elsevierViewall">Map of Makassar city, Indonesia, with the population density of each sub-district.</p>" ] ] 1 => array:7 [ "identificador" => "fig0010" "etiqueta" => "Figure 2" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr2.jpeg" "Alto" => 920 "Ancho" => 1508 "Tamanyo" => 77788 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0030" class="elsevierStyleSimplePara elsevierViewall">The number of DF incidences in Makassar city, Indonesia based on sub-district for the period of 2015–2017.</p>" ] ] 2 => array:7 [ "identificador" => "fig0015" "etiqueta" => "Figure 3" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr3.jpeg" "Alto" => 1153 "Ancho" => 1524 "Tamanyo" => 77571 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0035" class="elsevierStyleSimplePara elsevierViewall">Adjacency matrix for Makassar city, Indonesia.</p>" ] ] 3 => array:7 [ "identificador" => "fig0020" "etiqueta" => "Figure 4" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr4.jpeg" "Alto" => 825 "Ancho" => 2508 "Tamanyo" => 123788 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0040" class="elsevierStyleSimplePara elsevierViewall">Posterior densities plots of the significant parameter for DF survival data in the Makassar city, Indonesia.</p>" ] ] 4 => array:7 [ "identificador" => "fig0025" "etiqueta" => "Figure 5" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr5.jpeg" "Alto" => 1595 "Ancho" => 2508 "Tamanyo" => 271425 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0045" class="elsevierStyleSimplePara elsevierViewall">History iteration plots of the significant parameter for DF survival data in the city of Makassar, Indonesia.</p>" ] ] 5 => array:7 [ "identificador" => "fig0030" "etiqueta" => "Figure 6" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr6.jpeg" "Alto" => 1864 "Ancho" => 2167 "Tamanyo" => 372052 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0050" class="elsevierStyleSimplePara elsevierViewall">Posterior mean CAR frailties model with covariates for Makassar county level DF survival data.</p>" ] ] 6 => array:7 [ "identificador" => "fig0035" "etiqueta" => "Figure 7" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr7.jpeg" "Alto" => 1247 "Ancho" => 1508 "Tamanyo" => 70211 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0055" class="elsevierStyleSimplePara elsevierViewall">Estimated of the posterior survival function <span class="elsevierStyleItalic">S</span>(<span class="elsevierStyleItalic">t</span>) for DF data with age and grade variables.</p>" ] ] 7 => array:8 [ "identificador" => "tbl0005" "etiqueta" => "Table 1" "tipo" => "MULTIMEDIATABLA" "mostrarFloat" => true "mostrarDisplay" => false "detalles" => array:1 [ 0 => array:3 [ "identificador" => "at1" "detalle" => "Table " "rol" => "short" ] ] "tabla" => array:1 [ "tablatextoimagen" => array:1 [ 0 => array:2 [ "tabla" => array:1 [ 0 => """ <table border="0" frame="\n \t\t\t\t\tvoid\n \t\t\t\t" class=""><thead title="thead"><tr title="table-row"><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col" style="border-bottom: 2px solid black">Parameter \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col" style="border-bottom: 2px solid black">Mean \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col" style="border-bottom: 2px solid black">95% CI \t\t\t\t\t\t\n \t\t\t\t\t\t</th></tr></thead><tbody title="tbody"><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Intercept (β0) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">−4.297 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">(−4.951, −3.652) \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Sex (β1) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0.082 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">(−0.033, 0.187) \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Age (β2) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">−0.006 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">(−0.012, −0.0004) \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Grade (β3) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0.199 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">(0.079, 0.315) \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Haemoglobin (β4) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0.097 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">(−0.076, 0.269) \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Haematocrit (β5) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">−0.088 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">(−0.177, 0.003) \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Thrombocyte (β6) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">−0.022 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">(−0.091, 0.047) \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Leucocyte (β7) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">−0.049 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">(−0.161, 0.061) \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">ρ \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">2.473 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">(2.342, 2.607) \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">λ \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">3.15 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">(1.176, 6.335) \t\t\t\t\t\t\n \t\t\t\t</td></tr></tbody></table> """ ] "imagenFichero" => array:1 [ 0 => "xTab2564114.png" ] ] ] ] "descripcion" => array:1 [ "en" => "<p id="spar0060" class="elsevierStyleSimplePara elsevierViewall">Summary of posterior estimated parameters for spatial survival for DF survival data.</p>" ] ] 8 => array:8 [ "identificador" => "tbl0010" "etiqueta" => "Table 2" "tipo" => "MULTIMEDIATABLA" "mostrarFloat" => true "mostrarDisplay" => false "detalles" => array:1 [ 0 => array:3 [ "identificador" => "at2" "detalle" => "Table " "rol" => "short" ] ] "tabla" => array:1 [ "tablatextoimagen" => array:1 [ 0 => array:2 [ "tabla" => array:1 [ 0 => """ <table border="0" frame="\n \t\t\t\t\tvoid\n \t\t\t\t" class=""><thead title="thead"><tr title="table-row"><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col" style="border-bottom: 2px solid black">Model \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col" style="border-bottom: 2px solid black">pD \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col" style="border-bottom: 2px solid black">DIC \t\t\t\t\t\t\n \t\t\t\t\t\t</th></tr></thead><tbody title="tbody"><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Spatial survival \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">13.5 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">3698 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Non-spatial survival \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">9.115 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="char" valign="\n \t\t\t\t\ttop\n \t\t\t\t">3725 \t\t\t\t\t\t\n \t\t\t\t</td></tr></tbody></table> """ ] "imagenFichero" => array:1 [ 0 => "xTab2564113.png" ] ] ] ] "descripcion" => array:1 [ "en" => "<p id="spar0065" class="elsevierStyleSimplePara elsevierViewall">The values of pD and DIC for survival spatial and non-spatial models.</p>" ] ] 9 => array:6 [ "identificador" => "eq0005" "etiqueta" => "(1)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "h(tij;xij)=h0(tij) exp(βTxij)" "Fichero" => "STRIPIN_si16.jpeg" "Tamanyo" => 2026 "Alto" => 18 "Ancho" => 183 ] ] 10 => array:6 [ "identificador" => "eq0010" "etiqueta" => "(2)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "h(tij;xij)=ρtijρ−1 exp (βTxij+Wi)." "Fichero" => "STRIPIN_si23.jpeg" "Tamanyo" => 2260 "Alto" => 22 "Ancho" => 224 ] ] 11 => array:6 [ "identificador" => "eq0015" "etiqueta" => "(3)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "W|λ∼CAR(λ)." 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| 2022 Noviembre | 78 | 47 | 125 |
| 2022 Octubre | 66 | 35 | 101 |
| 2022 Septiembre | 39 | 43 | 82 |
| 2022 Agosto | 51 | 70 | 121 |
| 2022 Julio | 56 | 69 | 125 |
| 2022 Junio | 46 | 49 | 95 |
| 2022 Mayo | 50 | 57 | 107 |
| 2022 Abril | 39 | 52 | 91 |
| 2022 Marzo | 55 | 56 | 111 |
| 2022 Febrero | 45 | 51 | 96 |
| 2022 Enero | 41 | 44 | 85 |
| 2021 Diciembre | 48 | 50 | 98 |
| 2021 Noviembre | 42 | 64 | 106 |
| 2021 Octubre | 56 | 64 | 120 |
| 2021 Septiembre | 57 | 56 | 113 |
| 2021 Agosto | 30 | 34 | 64 |
| 2021 Julio | 62 | 26 | 88 |
| 2021 Junio | 58 | 26 | 84 |
| 2021 Mayo | 69 | 58 | 127 |
| 2021 Abril | 87 | 102 | 189 |
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